Modular arithmetic

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Odd Stones

Age

14 to 16

Challenge level

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.
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Days and Dates

Age

11 to 14

Challenge level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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Round and Round and Round

Age

11 to 14

Challenge level

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?
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Elevenses

Age

11 to 14

Challenge level

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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How Much Can We Spend?

Age

11 to 14

Challenge level

A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
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Going Round in Circles

Age

11 to 14

Challenge level

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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What Numbers Can We Make?

Age

11 to 14

Challenge level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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Where Can We Visit?

Age

11 to 14

Challenge level

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: ×2 and -5. What do you think?
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Favourite

What Numbers Can We Make Now?

Age

11 to 14

Challenge level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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Differences

Age

11 to 14

Challenge level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?